We present observations of the UV absorption lines in the Seyfert 1 galaxy NGC 3516 , obtained at a resolution of \lambda / \Delta \lambda \approx 40,000 with the Space Telescope Imaging Spectrograph ( STIS ) on 2000 October 1 . The UV continuum was \sim 4 times lower than that observed during 1995 with the Goddard High Resolution Spectrograph ( GHRS ) , and the X-ray flux from a contemporaneous Chandra X-ray Observatory ( CXO ) observation was a factor of \sim 8 below that observed with ASCA . The STIS spectra show kinematic components of absorption in Ly \alpha , C IV , and N V at radial velocities of - 376 , - 183 , and - 36 km s ^ { -1 } ( components 1 , 2 , and 3 + 4 , respectively ) , which were detected in the earlier GHRS spectra ; the last of these is a blend of two GHRS components that have increased greatly in column density . Four additional absorption components have appeared in the STIS spectra at radial velocities of - 692 , - 837 , - 994 , and - 1372 km s ^ { -1 } ( components 5 through 8 ) ; these may also have been present in earlier low-flux states observed by the International Ultraviolet Explorer ( IUE ) . Based on photoionization models , we suggest that the components are arranged in increasing radial distance in the order , 3 + 4 , 2 , 1 , followed by components 5 – 8 . We have achieved an acceptable fit to the X-ray data using the combined X-ray opacity of the UV components 1 , 2 and 3 + 4 . By increasing the UV and X-ray fluxes of these models to match the previous high states , we are able to match the GHRS C IV column densities , absence of detectable C IV absorption in components 5 through 8 , and the 1994 ASCA spectrum . We conclude that variability of the UV and X-ray absorption in NGC 3516 is primarily due to changes in the ionizing flux .